Concepts Of Physics MCQ Edition [Volume 2]PhysicsThe Special Theory of Relativity
Determine the mass, the kinetic energy, and the momentum of an electron travelling at 0.8c .
Options
- A9.1 10⁻³¹ kg , 2.6 10⁻¹⁴ J , 2.18 10⁻²² kg m s ⁻¹
- B15.2 10⁻³¹ kg , 13.6 10⁻¹⁴ J , 3.65 10⁻²² kg m s ⁻¹
- C15.2 10⁻³¹ kg , 4.4 10⁻¹⁴ J , 3.65 10⁻²² kg m s ⁻¹
- D15.2 10⁻³¹ kg , 5.5 10⁻¹⁴ J , 3.65 10⁻²² kg m s ⁻¹
Correct answer
D. 15.2 10⁻³¹ kg , 5.5 10⁻¹⁴ J , 3.65 10⁻²² kg m s ⁻¹
Step-by-step solution
The rest mass of an electron is m₀ = 9.1 10⁻³¹ kg . The relativistic factor is given by: = 1 1 - v^2 c^2 = 1 1 - (0.8)^2 = 1 0.6 = 5 3 The relativistic mass m is: m = m₀ = 5 3 9.1 10⁻³¹ kg 15.2 10⁻³¹ kg The kinetic energy K is: K = ( - 1)m₀ c^2 = ( 5 3 - 1 ) 9.1 10⁻³¹ (3 10^8)^2 K = 2 3 9.1 10⁻³¹ 9 10¹⁶ = 54.6 10⁻¹⁵ J 5.5 10⁻¹⁴ J The momentum p is: p = mv = ( 5 3 9.1 10⁻³¹ ) (0.8 3 10^8) p = 36.4 10⁻²³ kg m s ⁻¹ 3.65 10⁻²² kg m s ⁻¹